Immersing complete digraphs
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Publication:427820
DOI10.1016/J.EJC.2012.02.002zbMATH Open1243.05092arXiv1109.3741OpenAlexW1995632009MaRDI QIDQ427820
Author name not available (Why is that?)
Publication date: 18 June 2012
Published in: (Search for Journal in Brave)
Abstract: We consider the problem of immersing the complete digraph on t vertices in a simple digraph. For Eulerian digraphs, we show that such an immersion always exists whenever minimum degree is at least t(t-1), and for t at most 4 minimum degree at least t-1 suffices. On the other hand, we show that there exist non-Eulerian digraphs with all vertices of arbitrarily high in- and outdegree which do not contain an immersion of the complete digraph on 3 vertices. As a side result, we obtain a construction of digraphs with large outdegree in which all cycles have odd length, simplifying a former construction of such graphs by Thomassen.
Full work available at URL: https://arxiv.org/abs/1109.3741
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